# Dynamics of Two Vortex Rings in a Bose – Einstein Condensate

*2022, Volume 27, Number 6, pp. 713-732*

Author(s):

**Artemova E. M., Kilin A. A.**

In this paper, we consider the dynamics of two interacting point vortex rings in
a Bose – Einstein condensate. The existence of an invariant manifold corresponding to vortex
rings is proved. Equations of motion on this invariant manifold are obtained for an arbitrary
number of rings from an arbitrary number of vortices. A detailed analysis is made of the case
of two vortex rings each of which consists of two point vortices where all vortices have same
topological charge. For this case, partial solutions are found and a complete bifurcation analysis
is carried out. It is shown that, depending on the parameters of the Bose – Einstein condensate,
there are three different types of bifurcation diagrams. For each type, typical phase portraits
are presented.

Access to the full text on the Springer website |